Valence Sum Rule Research Articles

The first occurrence of the carbide anion, C4–, in an oxide mineral: Mikecoxite, ideally (CHg4)OCl2, from the McDermitt open-pit mine, Humboldt County, Nevada, U.S.A.

AbstractMikecoxite, ideally (CHg4)OCl2, is the first mercury-oxide-chloride-carbide containing a C4– anion coordinated by four Hg atoms (a permercurated methane derivative) to be described as a mineral species. It was found at the McDermitt open-pit mine on the eastern margin of the McDermitt Caldera, Humboldt County, Nevada, U.S.A. It is monoclinic, space group P21/n, Z = 4; a = 10.164(5), b = 10.490(4), c = 6.547(3) Å, V 698.0(5) Å3. Chemical analysis by electron microprobe gave Hg 86.38, Cl 11.58, Br 0.46, C 1.81, sum = 100.23 wt%, and O was detected but the signal was too weak for quantitative chemical analysis. The empirical formula, calculated on the basis of Hg + Cl + Br = 6 apfu, is (C1.19Hg3.39)(Cl2.57Br0.05)Σ2.62, and the ideal formula based on the chemical analysis and the crystal structure is (CHg4)OCl2. The seven strongest lines in the X-ray powder diffraction pattern are [d (Å), I, (hkl)]: 2.884, 100, (230); 2.989, 81, (301, 301, 112, 112, 131, 131); 2.673, 79, (122, 122, 212, 212); 1.7443, 40, (060, 432, 432); 5.49, 34, (101, 101); 4.65, 32, (120); 2.300, 30, (312, 312). The Raman spectrum shows three bands at 638, 675, and 704 cm–1, well above the range characteristic of NHg4 stretching vibrations between 540 and 580 cm–1, that are assigned to CHg4 stretching vibrations. Mikecoxite forms intergrowths of bladed crystals up to 100 μm long that occur on granular quartz or in vugs associated with kleinite. It is black with a submetallic to metallic luster and strong specular reflections and does not fluoresce under short-or long-wave ultraviolet light. Neither cleavage nor parting were observed, and the calculated density is 8.58 g/cm3. In the crystal structure of mikecoxite, (C4–Hg42+) groups link through O2– ions to form three-membered rings that polymerize into corrugated [CHg4OCl]+ layers with near-linear C4––Hg2+–O and C 4––Hg2+–Cl linkages. The layers link in the third direction directly via weak Hg2+–O2– and Hg2+–Cl– bonds to adjacent layers and also indirectly via interlayer Cl–. A bond-valence parameter has been derived for (Hg2+–C4–) bonds: Ro = 2.073 Å, b = 0.37, which gives bond-valence sums at the C4– ions in accord with the valence-sum rule. The source of carbon for mikecoxite in the volcanic high-desert environment of the type locality seems to be methane, with the reaction catalyzed by microbiota through full mercuration of carbon atoms, beyond the first stage that produces the volatile and highly mobile methylmercury, [CH3Hg]+, a potent neurotoxin that accumulates in marine food chains. Both the mineral and the mineral name have been approved by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (IMA 2021-060). The mineral is named after Michael F. Cox (b. 1958), a founding member of the New Almaden Quicksilver County Park Association (NAQCPA) who was responsible for characterizing and remediating environmental mercury on-site and who recovered the rock containing the new mineral.

Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (TO4)n- tetrahedra.

Chain, ribbon and tube silicates are based on one-dimensional polymerizations of (TO4)n- tetrahedra, where T = Si4+ plus P5+, V5+, As5+, Al3+, Fe3+ and B3+. Such polymerizations may be represented by infinite graphs (designated chain graphs) in which vertices represent tetrahedra and edges represent linkages between tetrahedra. The valence-sum rule of bond-valence theory limits the maximum degree of any vertex to 4 and the number of edges linking two vertices to 1 (corner-sharing tetrahedra). The unit cell (or repeat unit) of the chain graph generates the chain graph through action of translational symmetry operators. The (infinite) chain graph is converted into a finite graph by wrapping edges that exit the unit cell such that they link to vertices within the unit cell that are translationally equivalent to the vertices to which they link in the chain graph, and the wrapped graph preserves all topological information of the chain graph. A symbolic algebra is developed that represents the degree of each vertex in the wrapped graph. The wrapped graph is represented by its adjacency matrix which is modified to indicate the direction of wrapped edges, up (+c) or down (-c) along the direction of polymerization. The symbolic algebra is used to generate all possible vertex connectivities for graphs with ≤8 vertices. This method of representing chain graphs by finite matrices may now be inverted to generate all non-isomorphic chain graphs with ≤8 vertices for all possible vertex connectivities. MatLabR2019b code is provided for computationally intensive steps of this method and ∼3000 finite graphs (and associated adjacency matrices) and ∼1500 chain graphs are generated.

Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

AbstractSince their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii.We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction.Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures.In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges.We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2− and selenite (Se4+O3)2−] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.

Proof That a Dominant Endmember Formula Can Always Be Written for a Mineral or a Crystal Structure

ABSTRACTAn endmember formula must be: (1) conformable with the crystal structure of the mineral, (2) electroneutral (i.e., not carry a net electric charge), and (3) irreducible [i.e., not capable of being factored into components that have the same bond topology (atomic arrangement) as that of the original formula]. The stoichiometry of an endmember formula must match the “stoichiometry” of the sites in the structure; for ease of expression, I denote such a formula here as a chemical endmember. In order for a chemical endmember to be a true endmember, the corresponding structure must obey the valence-sum rule of bond-valence theory. For most minerals, the chemical endmember and the (true) endmember are the same. However, where local order would lead to strong deviation from the valence-sum rule for some local arrangements, such arrangements cannot occur and the (true) endmember differs from the chemical endmember. I present heuristic and algebraic proofs that a specific chemical formula can always be represented by a corresponding dominant endmember formula. That dominant endmember may be derived by calculating the difference between the mineral formula considered and all of the possible endmember compositions; the endmember formula which is closest to the mineral formula considered is the dominant endmember.

NNNPDF2.0: quark flavor separation in nuclei from LHC data

We present a model-independent determination of the nuclear parton distribution functions (nPDFs) using machine learning methods and Monte Carlo techniques based on the NNPDF framework. The neutral-current deep-inelastic nuclear structure functions used in our previous analysis, nNNPDF1.0, are complemented by inclusive and charm-tagged cross-sections from charged-current scattering. Furthermore, we include all available measurements of W and Z leptonic rapidity distributions in proton-lead collisions from ATLAS and CMS at sqrt{s} = 5.02 TeV and 8.16 TeV. The resulting nPDF determination, nNNPDF2.0, achieves a good description of all datasets. In addition to quantifying the nuclear modifications affecting individual quarks and antiquarks, we examine the implications for strangeness, assess the role that the momentum and valence sum rules play in nPDF extractions, and present predictions for representative phenomenological applications. Our results, made available via the LHAPDF library, highlight the potential of high-energy collider measurements to probe nuclear dynamics in a robust manner.

The Crystal Structure of Polylithionite-1M from Darai-Pioz, Tajikistan: the Role of Short-range Order in Driving Symmetry Reduction in 1M Li-rich Mica

AbstractThe crystal structure of polylithionite-1M from Darai-Pioz, (K0.97Na0.03Rb0.01)Σ1.01(Li2.04Al0.84 Ti4+0.09Fe3+0.03)Σ3.00(Si3.98Al0.02)O10[F1.68(OH)0.33]Σ2, a 5.1974(4), b 8.9753(6), c 10.0556(7) Å, β 100.454(1)°, V 461.30(6) Å3, space group C2, Z = 2, was refined to R1 = 1.99% using MoKα X-radiation. In the space group C2, there are three octahedrally coordinated M sites in the 1M mica structure: the M(1) site is occupied by Li+ and minor vacancy that is likely locally associated with Ti4+ at the M(2) site; the M(2) site is occupied dominantly by Al3+, with other minor divalent to tetravalent cations; the M(3) site is completely occupied by Li+. In the space group C2, the structure is completely ordered. Each non-bridging O2– ion is surrounded by an ordered arrangement of 2Li+ + Al3+ + Si4+ with an incident bond-valence sum of 1.95 vu (valence units). The F– ion is coordinated by Li+ + Li+ + Al3+ with an incident bond-valence sum of 0.84 vu (values around F– generally tend to be lower than ideal). Thus, the valence-sum rule is satisfied, both long range and short range. In the space group C2/m, there is long-range order but not short-range order. There are three different short-range arrangements, one of which has bond-valence deficiencies of 0.38 and 0.49 vu around the non-bridging O2– ion and the F– ion, destabilizing the structure relative to the more ordered arrangement of the C2 structure, which conforms more closely to the valence-sum rule. The drive to lower the symmetry in polylithionite-1M from C2/m to C2 comes from the short-range bond-valence requirements of the structure.

A priori bond-valence and bond-length calculations in rock-forming minerals

Within the framework of the bond-valence model, one may write equations describing the valence-sum rule and the loop rule in terms of the constituent bond valences. These are collectively called the network equations, and can be solved for a specific bond topology to calculate its a priori bond valences. A priori bond valences are the ideal values of bond strengths intrinsic to a given bond topology that depend strictly on the formal valences of the ion at each site in the structure, and the bond-topological characteristics of the structure (i.e. the ion connectivity). The a priori bond valences are calculated for selected rock-forming minerals, beginning with a simple example (magnesiochromite, = 1.379 bits per atom) and progressing through a series of gradually more complex minerals (grossular, diopside, forsterite, fluoro-phlogopite, phlogopite, fluoro-tremolite, tremolite, albite) to finish with epidote (= 4.187 bits per atom). The effects of weak bonds (hydrogen bonds, long Na+—O2− bonds) on the calculation of a priori bond valences and bond lengths are examined. For the selected set of minerals, a priori and observed bond valences and bond lengths scatter closely about the 1:1 line with an average deviation of 0.04 v.u. and 0.048 Å and maximum deviations of 0.16 v.u. and 0.620 Å. The scatter of the corresponding a priori and observed bond lengths is strongly a function of the Lewis acidity of the constituent cation. For cations of high Lewis acidity, the range of differences between the a priori and observed bond lengths is small, whereas for cations of low Lewis acidity, the range of differences between the a priori and observed bond lengths is large. These calculations allow assessment of the strain in a crystal structure and provide a way to examine the effect of bond topology on variation in observed bond lengths for the same ion-pair in different bond topologies.

Empirical electronic polarizabilities: deviations from the additivity rule. I. M2+SO4·nH2O, blödite Na2M2+(SO4)2·4H2O, and kieserite-related minerals with sterically strained structures

Empirical electronic polarizabilities allow the prediction of total mineral polarizabilities and mean refractive indices of the vast majority of minerals and synthetic oxides. However, deviations from the valence-sum rule at cations in some minerals are associated with large deviations of observed from calculated total polarizabilities. We have identified several groups of minerals and compounds where deviations from the valence-sum rule at cations lead to polarizability deviations of 2–5%: M(SO4)·nH2O, n = 1–6, blodite-group minerals [Na2M2+(SO4)2·4H2O], and the kieserite-related minerals: isokite, panasqueiraite and tilasite. In these minerals, the environment of the M ions contains both O and H2O: Mg[O4(H2O)2] in kieserite, szmikite, and szomolnokite; Mg[O2(H2O)4] in starkeyite, ilesite, and rozenite, and Mg[(H2O)6] in hexahydrite. In compounds where the ligands are only H2O, deviations from the valence-sum rule at the M(H2O)6 groups are not accompanied by significant polarizability deviations. This is the case for epsomite, MgSO4·7H2O; bieberite, CoSO4·7H2O; goslarite, ZnSO4·7H2O, six silicofluorides, MSiF6·6H2O; eighteen Tutton’s salts, M2M′(SO4)2·6H2O, where M = K, Rb, Cs and M′ = Mg, Mn, Fe, Co, Ni, Cu, and Zn; and eleven MM′(SO4)2·12H2O alums, where M = Na, K, Rb and Cs, and M′ = Al, Cr, Ga and In. This is also the case for the sulfates alunogen, Al2(SO4)3·17H2O and halotrichite, FeAl2(SO4)4·22H2O; three hydrated nitrates; one phosphate; three antimonates and two hydrated perchlorates. A possible explanation for this different behavior is that the bond-valence model treats O and H separately, whereas polarizability calculations treat the polarizability of the entire H2O molecule.

Short-range atomic arrangements in minerals. I: The minerals of the amphibole, tourmaline and pyroxene supergroups

Spectroscopy is a key aspect of deriving local arrangements of atoms in minerals. Vibrational spectroscopy in the principal O–H-stretching region and MAS NMR spectroscopy are sensitive to such local arrangements, and play a crucial role in characterizing local structure in minerals in which there is solid solution. Variation in local arrangements of ions around a “probe” ion such as (OH)− can produce shifts in the energy of the principal O–H-stretching frequency, providing a window into those local arrangements. Similarly, variation in local arrangements around a “probe” isotope such as 27Al or 29Si can produce shifts in resonance energy that are indicative of differences in local environment. It is useful to develop a configuration symbol for the structural environment of the probe species, i.e. , the configuration of nearest-neighbour and next-nearest-neighbour polyhedra/sites, and then the local arrangements of atoms may be expressed in terms of this configuration symbol. Work on the monoclinic C 2/ m amphiboles, tourmaline and monoclinic pyroxene is reviewed here in terms of the particular effects that can give rise to absorptions in the principal O–H-stretching region of vibrational spectra. It is notable that the nearest-neighbour configurations in the amphibole, tourmaline and mica structures are topologically identical, and hence there should be strong spectral characteristics that are common to minerals of all three structure types. The spectra of the C 2/ m amphiboles show strong next-nearest-neighbour effects, and one expects such effects to occur also in spectra of minerals of the tourmaline (and mica) supergroups. The valence-sum rule of local bond-valence theory provides a strong constraint on possible local arrangements involved in heterovalent solid-solution in these minerals.

Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.

Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra. Values of the RMSD range from 0.033-2.451 v.u. (1.1-40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond-valence parameters in this paper. Two common methods for the derivation of bond-valence parameters have been evaluated: (1) fixing B and solving for R(o); (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixing B at 0.37 Å leads to a mean weighted-RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond-valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted-RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple-coordination ions. The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence-bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond-valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond-valence sums using the GRG method and our complete data set.

Bond valence at mixed occupancy sites. I. Regular polyhedra.

Bond valence sum calculations at mixed occupancy sites show the occurrence of systematic errors leading to apparent violations of the Valence Sum Rule (bond valence theory) in regular and unstrained bonding environments. The systematic deviation of the bond valence from the expected value is observed in the long-range structure, and is discussed from geometric and algebraic viewpoints. In the valence-length diagram, such a deviation arises from discrepancies between the intersection points of the long-range bond valences and the theoretical bond valences with the valence-length curves of involved cations. Three factors cause systematic errors in the bond valences: difference in atomic valences, bond valence parameters Ri (the length of a bond of unit valence) and bond valence parameters bi (the bond softness) between the involved cations over the same crystallographic site. One important consequence strictly related to the systematic errors is that they lead to erroneous bond strain values for mixed occupancy sites indicating underbonding or overbonding that actually does not exist.

Survey of Bond Lengths in the Solid State for Oxides: Results and Applications

A complete survey of bond lengths from the Inorganic Crystal Structure Database (ICSD) is presented for all atoms of the Periodic Table of Elements, bonded to oxygen and in different oxidation states and coordination numbers. From over 135,000 crystal structures, a total of 33,343 coordination polyhedra and 188,462 bond distances were collected after passing a rigorous filtering process. One hundred thirty-six (136) ions in four hundred seventy-three (473) different configurations (coordination numbers) resulted. First, the bondlength distributions are visually inspected. This leads to (1) the observation and visual interpretation of known phenomena (e.g. Jahn-Teller effect), and (2) the isolation of new phenomena, as trends that are less obvious in smaller case-studies become more noticeable. Next, different applications of the data are investigated. The completeness of the survey allows the reassessment of important parameters of the solid state: ionic radii, and bond-valence parameters. Of the 473 ionic radii derived in this study, 329 revisions are made to Shannon's list of radii [1] (of which 176 were estimates), and 144 new ionic radii are derived. Next, a systematic evaluation of all bond-valence parameters published to date is done for oxides. Furthermore, using a new method of derivation, 136 new pairs of bond-valence parameters are obtained. In comparison to the previous-best published bond-valence parameters, an overall average decrease in the r.m.s.d. to the valence-sum rule of 20.7% (12.6% when weighted) is observed for the 33,343 coordination polyhedra, using the new parameters. New equations to describe the bond-length to bond-valence relation are also investigated. From an optimization between the experimental and a priori bond-valences of 54 carefully-selected crystal structures, roughly 20 relatively simple equations were selected for testing. Following a rigorous evaluation, the current exponential equation was found to be a viable choice in describing the relation. Finally, bond-length and bond-valence ranges are assigned to the 473 configurations of the atoms. Whereas the bondlength ranges are a useful aid in structure refinement, the assignment of a bond-valence range to ions allows a priori analysis of site occupancy in crystal structures.

Raman Spectrum of Vanadium-Zirconia Yellow Pigment

ABSTRACT Monoclinic vanadium-zirconia yellow pigments were prepared by gelling mixtures of zirconium n-propoxide and vanadyl acetylacetone. The nature of interactions between the host ion and the foreign cation in the vanadium-zirconia pigment was investigated in order to contribute to a better understanding of the origin of this pigmenting system using Raman scattering measurements. The Raman spectra of powdered samples of the vanadium-zirconia pigment recorded between 100 and 1400 cm−1 show the peaks at 991, 701, and 403 cm−1 assigned to the asymmetric and symmetric stretching and bending vibrations of the V4+ = O bonds, respectively. The assignment of these peaks was discussed by comparison with Raman spectra of vanadium oxides and on the basis of V-O bond distances deduced from the Hardcastle and Wachs equation and from the valence state of the vanadium cation calculated by Brown in the valence sum rule. This suggests that the V4+ cations replace Zr4+ in sevenfold coordinated site in the monoclinic zirconia structure. The V4+ cation allowing the d-d electronic transition is related to the origin of the lemon yellow coloration.

The crystal structure of comancheite, Hg2+55N3–24 (OH,NH2)4(Cl,Br)34, and crystal-chemical and spectroscopic discrimination of N3– and O2– anions in Hg2+ compounds

AbstractThe crystal structure of comancheite, Hg2+55N3–24(OH, NH2)4(Cl,Br)34, orthorhombic, space group Pnnm, a = 18.414(5), b = 21.328(6), c = 6.6976(19) Å, V = 2630(2) Å3, Z = 1, was solved by direct methods and refined to an R1 index of 4.3% based on 4160 unique observed reflections. In the structure of comancheite, there are nine crystallographically distinct Hg2+ cations, each of which is coordinated by two N3– anions to form near-linear N3––Hg2+–N3– groups. Four other crystallographically distinct Hg2+ cations are coordinated by a mixture of N3–, O2–, (OH)– and (NH2)– anions, and there is a small amount of [Hg–Hg]2+ dimer. In addition, there are eight crystallographically distinct halogen sites, three of which are completely occupied by Cl–, and five of which are occupied by both Cl– and Br–. The principal anion, N3–, shows a strong preference for tetrahedral coordination by Hg2+, which results in a strongly bonded three-dimensional {–Hg2+–N3––} framework. This framework is both interrupted and contains large interstices that incorporate additional Hg2+ cations, a very small amount of [Hg+–Hg+]2+ dimer and additional anion species, O2–, (OH)– and (NH2)–, that coordinate Hg2+.Comancheite was described originally as an Hg-oxide mineral. The major change in chemical composition indicated by the present work was approved by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (Voting Proposal 13-B). The presence of N provides some analytical challenges, particularly in the presence of Hg. New bond-valence parameters were derived for Hg2+–N3– bonds [Ro(N3–) = 1.95] using well refined Hg2+ structures, and this allows discrimination between Hg2+–O2– and Hg2+–N3– bonds based on the valence-sum rule. Comparison of the Raman spectra of several Hg-bearing minerals shows that peaks in the range 500–700 cm–1 are characteristic of Hg2+–N3– stretching vibrations whereas peaks in the range 350–500 cm–1 are characteristic of Hg2+–O2– stretching vibrations; Hg2+–O2– and Hg2+ – N3– bonds may be discriminated on this basis.

The crystal structure of chalcoalumite: mechanisms of Jahn-Teller-driven distortion in [6]Cu2+-containing oxysalts

AbstractThe crystal structure of chalcoalumite, ideally Cu2+Al4(SO4)(OH)12(H2O)3, monoclinic, P21/n, Z = 4:a 10.228(3), b 8.929(3), c 17.098(6) Å, β 95.800(11)°, V 1553.6(1.5) Å3, has been refined to R1 = 3.08% for 4,022 unique observed (4σ) reflections collected on a Bruker D8 three-circle diffractometer equipped with a rotating-anode generator, multilayer optics and an APEX-II CCD detector. In the structure of chalcoalumite, there is one S site, tetrahedrally coordinated by four O anions, with <S–O> = 1.472 Å. There are four Al sites with site-scattering values in accord with occupancy by Al and <Al–O> distances of 1.898–1.919 Å. There is one Cu site occupied by Cu2+ and coordinated by six anions in the [4 + 2] arrangement typical for octahedrally coordinated Cu2+. The short <Cu–O> distance of 2.086 Å is in accord with the low degree of bond-length distortion of the Cu octahedron. There are 19 anion sites: 4 sites are occupied by O atoms that are bonded to the S cation, 12 sites are occupied by (OH) groups that bond to all octahedrally coordinated cations, and 3 sites are occupied by (H2O) groups that are held in the structure solely by hydrogen bonding. The structure of chalcoalumite consists of interrupted sheets of edge-sharing Al and Cu octahedra of the form [Cu2+Al4(OH)12]2+ that intercalate layers of (SO4) tetrahedra and (H2O) groups. Chalcoalumite is a member of the nickelalumite group.Cu2+ϕ6(ϕ = O2–, (OH)–, (H2O)0) octahedra show a wide range of bond-length distortion away from the holosymmetric arrangement, driven by spontaneous symmetry-breaking of the degenerate electronic ground-state in holosymmetric octahedral coordination. Here, we examine the structural mechanisms that allow large octahedron distortions of this type. There are two mechanisms: (1) coupling of (usually parallel) octahedron distortions to a vibrational phonon, inducing a (often ferroelastic) phase transition in M2+-Cu2+ solid-solutions; (2) cooperative orientational disorder, where bond topology (polyhedron linkage) allows large differences in bond lengths within polyhedra to accord with the valence-sum rule of bond-valence theory.

The role of H2O in controlling bond topology:I. The[6]Mg(SO4)(H2O)n(n= 0–11) structures

AbstractHere, we examine the role of (H2O) in controlling polymerization of structural units in simple hydrated oxysalt compounds of the form Mg(SO4)(H2O)n. As the number of (H2O) groups in the structure increases, the number ofM—M(M= Mg) linkages decreases in a 1 : 1 ratio with the (increasing) number of (H2O) groups until noM—Mlinkages are left, and then the number ofM—T(T= S) linkages decreases with the (increasing) number of (H2O) groups until noM—Tlinkages are left (atn= 6). The change in bond topology is monotonic as a function of (H2O) content except forn= 5 where, instead of replacing anM—Tlinkage, the fifth (H2O) group is held in the structure by hydrogen bonds only. The valence-sum rule of bond-valence theory constrains the anion-coordination numbers to [2], [3] and [4] in these structures. The handshaking lemma of graph theory allows us to derive an equation relating the coordination numbers of the cations (Mg = [6], S6+= [4], H = [2]) to the coordination numbers of the anions. There are four integer solutions to this equation, and the Mg(SO4)(H2O)nstructures correspond to two of these solutions. Structures are known forn= 0–2.5, 4–7, 11; considering the variations in connectivity and coordination number as a function ofn, a possible structural arrangement is proposed for Mg(SO4)(H2O)3.

Phase Selection and Site-Selective Distribution by Tin and Sulfur in Supertetrahedral Zinc Gallium Selenides

Doping is among the most important methods to tune the properties of semiconductors. For dense phase semiconductors, the distribution of dopant atoms in crystal lattices is often random. However, when the size of semiconductors becomes increasingly smaller and reaches the extreme situation as is the case in chalcogenide supertetrahedral clusters, different chemically distinct sites (e.g., corner, edge, face, and core) occur, which can dramatically affect the doping chemistry at different sites and also spatial assembly of such clusters into covalent superlattices. In this work, we use the Zn-Ga-Se supertetrahedral clusters and their frameworks as the model system to examine the doping chemistry of Sn(4+) and S(2-) in the Zn-Ga-Se clusters. A series of selenide clusters (undoped supertetrahedral T4-ZnGaSe, S-doped T4-ZnGaSeS, Sn-doped T4-ZnGaSnSe, and dual S- and Sn-doped T4-ZnGaSnSeS) have been prepared with various levels of Sn- and S-doping and with different superlattice structures (OCF-1, -5, -40, and -42). The complex compositional and structural features of these materials are dictated by the convoluted interplay of three key factors: (1) the overall charge density and size/shape matching between clusters/frameworks and protonated guest amines determine the framework topology and the doping levels of Sn(4+) and S(2-); (2) the site selectivity of Sn(4+) is dictated by the local charge balance surrounding anionic Se/S sites as required by the electrostatic valence sum rule; and (3) the site selectivity and doping levels of sulfur is dictated by the location and amount of Sn based on hard soft acid base (HSAB) principle. The cooperative effect of amine-templating and doping by Sn and/or S leads to a rich chemical system with tunable framework compositions, topologies, and electronic properties.

Short-range constraints on chemical and structural variations in bavenite

AbstractBavenite is an orthorhombic calcium beryllium aluminosilicate, a ≈ 23.2, b ≈ 5.0, c ≈ 19.4 Å, V ≈ 2250 Å3, Z = 4, that crystallizes in the space group Cmcm. The crystal structures of 24 bavenite samples from various localities worldwide were refined to R1 values from 2.4 to 7.5% based on ∼1330 unique reflections collected with Mo-Kα X-radiation on a Bruker P4 CCD single-crystal diffractometer. The composition of each crystal was determined by electron microprobe analysis. There is extensive solid-solution in bavenite according to O(2)OH– + T(4)Si4+ + T(3)Be2+ ⇌ O(2)O2– + T(4)Al3+ + T(3)Si4+, such that the general formula may be written Ca4BexSi9Al4–xO28–x(OH)x, where x ranges from 2.00 to ∼3.00 a.p.f.u. Small amounts of additional Be may be incorporated into bavenite via the substitution T(3)Be + O(2)OH– + Na + T(4)Si2 ⇌ T(3)Si + O(2)O2– + Ca + T(4)Al2. Local (short-range) bond-valence considerations indicate that Short-Range Order (SRO) should be extensive in the bavenite structure, and this is confirmed by Fourier Transform Infrared (FTIR) spectroscopy in the principal OH-stretching region and by 27Al Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR) spectroscopy. Short-range bond-valence considerations indicate that the T(3)–T(4)–T(3)–T(4) rings of the framework can incorporate any short-range arrangement of cations consonant with their site populations [T(3) = Be,Si; T(4) = Si,Al], and 27Al MAS NMR spectroscopy confirms this, showing the presence of the local clusters T(3)Be–T(4)Al–T(3)Be, T(3)Si–T(4)Al–T(3)Be and T(3)Si–T(4)Al–T(3)Si. Incorporation of Be at the T(3) site is accompanied by local replacement of O2– by (OH)– at the O(2) site and hydrogen bonding to the adjacent O(3) anion; the latter promotes Be → Si substitution at the T(3) tetrahedron adjacent in the b direction. T(3)–T(4)–T(3)–T(4) rings link in the c direction through a T(3)–(1)–(3) linkage [T(1) = Si]. Local bond-valence considerations show that occupancy of both T(3) tetrahedra by Be violates the valence-sum rule, and that the linkage T(3)Be–T(1)Si–T(3)Si provides the constraint whereby Be does not exceed 3 a.p.f.u. in bavenite when incorporated via the substitution O(2)OH– + T(4)Si4+ + T(3)Be2+ ⇌ O(2)O2– + T(4)Al3+ + T(3)Si4+.

Octahedrally coordinated vacancies in tourmaline: a theoretical approach

AbstractBond-valence theory is used to explore the local arrangements involving vacancies at the Y and Z sites in the tourmaline structure. The local bond-valence requirements of all possible local arrangements around the O8, O7, O6, O3 and O1 anion-sites have been determined for Y- and Z-site vacancies locally associated with Li1+, Mg2+, Al3+, Fe2+, Fe3+, B3+ and Si4+. The results show that arrangements involving tetrahedrally coordinated TR3+-cations and octahedrally coordinated YR2+- and ZR2+-cations around O8, 07 and O6 can be ruled out, together with arrangements involving vacancies and YLi1+. As the occurrence of a Y-site vacancy (Y☐) is more in accord with the valence-sum rule than the occurrence of a Z-site vacancy (Z☐), Y☐ is more likely to occur than Z☐ in tourmaline. Local arrangements involving vacancies around O1- and O3-sites can be stable for OH−, but not for O2−. Of particular interest in this regard are the arrangements [YR3+YR3+Y☐]−O1(OH−) and [ZR3+ZR3+Y☐]−O3(OH−), which yield the smallest deviations from the valence-sum rule. Coupling these stable arrangements with 2 × [TSi4+ZR3+Y☐]−O6(O2−) forms larger vacancy clusters: [Y(R3+)2−O1(OH−)−y(☐)− O3(OH−)−O6(O2−)2−(ZR3+TSi4+)2]. In tourmaline, vacancies are more favoured to occur at Y rather than at Z, in tandem with OH− at O3 and O1, R3+ at Y and Z and Si4+ at T.

Hydrogen bonds in inorganic crystals: A microscopic study on the valence electron distribution of hydrogen in O–H···O systems

From the chemical bond viewpoint, we scrutinized the valence electron distribution of hydrogen in O–H···O systems in inorganic crystals. The influence of different crystalline environments on the original O–H bond lengths d 0 of O–H···O hydrogen bonds was quantitatively expressed by a function of d 0 versus the length of the constituent bonds. It is clearly shown that the valence electron distribution of hydrogen is affected evidently by the detailed environments of the O–H···O systems and the results agree well with the bond valence sum rule. Furthermore, the shortest O–H length in crystals is predicted to be 0.806 Å which is consistent with the value of 0.798 Å detected by neutron diffraction measurements. The current work establishes a bridge between structure and microscopic properties of hydrogen bonds, which can give us a useful clue to the utilization of hydrogen bonds in the design of inorganic functional materials.